Question 1

A company needs to sell a certain number of music units per month to break even. If the cost equation is $$8.1n + 2,900 = 20n + 6,600$$, what is the minimum number of units $$n$$ that must be sold to make a profit?

Accepted Answer

$$n \geq 260$$

Question 2

Factor the following expression completely: $$4x^2 + 12x$

Accepted Answer

$$4x(x + 3)$$

Question 3

Which of the following is the greatest common factor (GCF) of $$6x^2 - 24x$?

Accepted Answer

$$6x(x - 4)$$

Question 4

Factor the expression $$2m^2 + 8m$ by grouping.

Accepted Answer

$$2m(m + 4)$$

Question 5

Given the area of a shaded region as $$x(x + 2) - 3x(x)$$, which of the following is the simplified expression for the area?

Accepted Answer

$$-2x^2 + 2x$

Question 6

Which pair of integers multiplies to $$-24$$ and adds to $$-10$$?

Accepted Answer

$$-12$$ and $$2$$

Question 7

Factor the quadratic $$x^2 - 10x + 24$ completely.

Accepted Answer

$$(x - 6)(x - 4)$$

Question 8

Which of the following is the correct factorization of $$y^2 + y - 30$?

Accepted Answer

$$(y + 6)(y - 5)$$

Question 9

A rectangular garden has a length of $$x + 8$$ meters and a width of $$6x$$ meters. Write an expression for the area and factor it completely.

Accepted Answer

$$6x(x + 8)$$

Question 10

Which of the following is the correct factorization of $$x^2 + 7x + 12$?

Accepted Answer

$$(x + 3)(x + 4)$$

Question 11

If $$x^2 - 5x - 36 = 0$, what are the solutions for x$?

Accepted Answer

$$x = 9, x = -4$$

Question 12

Which of the following expressions is equivalent to $$2x^2 - 8x$?

Accepted Answer

$$2x(x - 4)$$

Question 13

Factor the expression $$x^2 - 16$ completely.

Accepted Answer

$$(x + 4)(x - 4)$$

Question 14

Which of the following is the correct factorization of $$f^2 + 2f - 35$?

Accepted Answer

$$(f + 7)(f - 5)$$

Question 15

Given $$x^2 + 5x + 6$, which of the following pairs of integers multiply to 6$ and add to 5$?

Accepted Answer

$$2$$ and $$3$$

Question 16

Which of the following is the correct factorization of $$g^2 + 2g - 35$?

Accepted Answer

$$(g + 7)(g - 5)$$

Question 17

If $$x^2 + 4x + 3 = 0$, what are the solutions for x$?

Accepted Answer

$$x = -1, x = -3$$

Question 18

Which of the following is the correct factorization of $$f^2 + 2f - 35$?

Accepted Answer

$$(f + 7)(f - 5)$$

Factoring and Common Factors in Intermediate Algebra

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